Not self can be seen in different ways.
Not self as in terms of existence.
In SN44.10, Buddha say if there is a self, he will side with the eternalist. Which means where is a permanent, unchanging existence of self. If he said there is no self, then he will side the annihilationists. Which means all existence ends.
Not self shows there is an existence which is not permanent and continues on the cycle of birth and death as long as kamma does not end.
Not Self in terms of powerless.
MN35
When you say thus: ‘Material form is my self,’ do you exercise any such power over that material form as to say: ‘Let my form be thus; let my form not be thus’?”
MN 141
19. “And what, friends, is ‘not to obtain what one wants is suffering’? To beings subject to birth there comes the wish: ‘Oh, that we were not subject to birth! That birth would not come to us!’ But this is not to be obtained by wishing, and not to obtain what one wants is suffering. To beings subject to ageing…subject to sickness…subject to death…subject to sorrow, lamentation, pain, grief, and despair, there comes the wish: ‘Oh, that we were not subject to sorrow, lamentation, pain, grief, and despair! That sorrow, lamentation, pain, grief, and despair would not come to us!’ But this is not to be obtained by wishing, and not to obtain what one wants is suffering.
Dispeller of Delusion (Abhidhamma commentary)
233. But it is no-self (anattã) in the sense of powerlessness. Or because there is no exercise of power in these three instances [namely,] “this being arisen, let it not reach presence; having reached presence, let it not grow old; having grown old, let it not break up”; and it is void of this quality of having power exercised over it (vasavattana). Therefore it is no-self for these four reasons [namely.] because it is void, because it has no owner, because of not behaving as desired (akamakariya) [and] because of exclusion of self.
In other words, if there is a self, one can don’t age, sick and die. One can be forever young and healthy and not die as one has power over existence.
Not self as stated categorically by Buddha
AN3.136
(3) “Bhikkhus, whether Tathagatas arise or not, there persists that law, that stableness of the Dhamma, that fixed course of the Dhamma: ‘All phenomena are non-self.’ A Tathagata awakens to this and breaks through to it, and then he explains it, teaches it, proclaims it, establishes it, discloses it, analyzes it, and elucidates it thus: ‘All phenomena are non-self.’”(phenomena here is the translation of dhamma)
Dhammapada Verse 279: “All phenomena (sankhara) are without Self”; when one sees this with Insight-wisdom, one becomes weary of dukkha (i.e., the khandhas). This is the Path to Purity.
These shows that dhamma is by nature not self. There is not a self to be found. It also indicates that not self is a not negation of a self. Rather it is wrong view that cause a view that there is a self in dhammas. And it is ignorance that blinds us for not seeing that the nature of dhammas which is not self.
